https://haifei-home.pages.dev/tags/%E5%85%8B%E6%B0%8F%E7%AC%A6/Recent content in 克氏符 on Haifei's HomeHugozh-CNhfwang132@gmail.com (hfwang132)hfwang132@gmail.com (hfwang132)This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.Sun, 27 Apr 2025 23:12:31 +0800https://haifei-home.pages.dev/post_20250427_%E5%85%8B%E6%B0%8F%E7%AC%A6%E5%88%B0%E5%BA%95%E6%98%AF%E4%B8%8D%E6%98%AF%E5%BC%A0%E9%87%8F/Sun, 27 Apr 2025 23:12:31 +0800hfwang132@gmail.com (hfwang132)https://haifei-home.pages.dev/post_20250427_%E5%85%8B%E6%B0%8F%E7%AC%A6%E5%88%B0%E5%BA%95%E6%98%AF%E4%B8%8D%E6%98%AF%E5%BC%A0%E9%87%8F/<p>个人最喜欢的理解是把 $\Gamma$ 看成标架丛上的联络，这样一来，克氏符的变换规则</p> <p>$\boxed{ \begin{aligned} \bar{\Gamma}^i_{\mu j} = \frac{\partial \bar{x}^i}{\partial x^k}\frac{\partial x^l}{\partial \bar{x}^j} \frac{\partial x^\nu}{\partial \bar{x}^\mu} \Gamma^k_{\nu l} \color{red}{ + \frac{\partial \bar{x}^i}{\partial x^k} \frac{\partial^2 x^k}{\partial x^\mu \partial \bar{x}^j}} \end{aligned} }$</p> <p>就只不过是一个规范变换：</p>